Do these conjoined twins share a mind?

In the New York Times, a piece by Susan Dominus on two twins joined at the head ("craniopagus") who are "beyond rare" because of the way their brains fused inside their skulls. "Their neural anatomy is unique, at least in the annals of recorded scientific literature," she writes. "Their brain images reveal what looks like an attenuated line stretching between the two organs, a piece of anatomy their neurosurgeon, Douglas Cochrane of British Columbia Children’s Hospital, has called a thalamic bridge, because he believes it links the thalamus of one girl to the thalamus of her sister."